Such a shame; only the second and third nuclear explosions ever led to peace. We should have done much more to provoke world peace.

On the contrary.
The war was already over at that point, Japan had lost all strategic points and was only fighting in fleeting desperation.
They chose to drop the bomb simply to show the Russians that we had it and we re willing to use it. Thus launching the cold war.

The war was already over at that point, Japan had lost all strategic points and was only fighting in fleeting desperation.

There is truth here.

In April of 1941, Japan and the Soviet Union signed a Neutrality Pact with one another. Despite the opposite alignments of the two empires (remember, the Russians were our allies), this treaty made good sense, particularly for the Japanese. It afforded them the opportunity to continue their war of expansion to the south and east (furthering their goal of establishing dominance in the Pacific), while assuaging the Russians of the fear that Japan's activities in China might creep further west into territory which would threaten the USSR's claims in western Asia.

By 1945, however, it was clear to Soviet leaders that Japan's conquest was at an end, and the idea began to be floated that, just as the USSR had successfully expanded its territory into eastern Europe, by entering the Pacific war on the side of the Allied powers at this late stage, they might stand to benefit by gaining control of certain territories in the Pacific region as well. Thus, in April of 1945, the Soviet Union denounced this pact and declared war on Japan, beginning with the invasion of Manchuria, a part of China which was then held by the Japanese.

This was, for all intents and purposes, the last nail in Japan's coffin. Japanese leaders, who had already begun to float the idea of surrender, now begun to conduct formal talks with the USSR through their ambassador in Switzerland. Why the USSR? Simple- the Soviets had no axe to grind. Most of the other Allied nations (the US not least among them) were by this point felt to be fighting for revenge. But because the USSR and Japan had not long been at conflict, and little in the way of atrocities had yet been committed (eg: no long history of horrific mistreatment of POWs or the like), it was felt by the Japanese that Russia would be least predisposed towards converting the act of surrender into a final grand show of retribution.

Now, from the standpoint of the US and its western Allies, this was not an acceptable state of affairs. Even before the war's end, Cold-war-style tensions had already begun to grow. Were Japan to surrender to the Soviet Union, the Soviets would be permitted to expand their empire even further, gaining a dangerous foothold in a region already afflicted by one communist government, and considered to be of dramatic strategic importance to the US. The East / West division of Germany, in particular, was a debacle that the US and Britain did not wish to see repeated.

With this perspective in mind, it becomes obvious why the US felt it imperative that the war be prolonged until such a time that Japan could be brought to unconditional surrender on America's terms, rather than allowing the Soviet Union to broker the terms of peace. The use of the atomic bomb did not provide the quickest possible conclusion of the war, but it did allow the US to ensure that the Soviets were excluded from the post-war settlement of Japan's territories.